Oh, absolutely! The quote you mention is a direct allusion to Shakespeare's Othello! Yes, I'll admit that it's not an exact quote (at least how you are relating it, anyway). It's a really wonderful thing to catch these allusions in the midst of a movie, actually. As Lionel said those words, I remembered that Iago was the one saying a similar quote, but I'll admit that I had to look up exactly where it was in the play.
The quote similar to the one you mention is in Act 3, Scene 3 of Othello. It's an all-important scene, of course, where Iago is purposely feeding Othello the seeds of jealousy, ... telling Othello to observe Cassio's behavior with Othello's wife, Desdemona. It is in the middle of this discourse that Iago says this:
Poor and content is rich, and rich enough; / But riches fineless is as poor as winter / To him that ever fears he shall be poor;-- / Good heaven, the souls of all my tribe defend / From jealousy!
Iago is saying here that one is more at peace if they are "poor" and "content." It is only is one is afraid to be poor that jealousy erupts. Now, of course, I know you didn't ask, ... but it should be your own delight to figure out how this little beauty of a quote fits in so well with The King's Speech.